Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

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Cambridge University Press, Apr 12, 2001 - Mathematics - 352 pages
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This is a thoroughly revised version of the successful first edition. In addition to up-dating the existing text, the author has added new material that will prove useful for research or application of the finite element method. The most important applications of this method receive an in-depth treatment in this book. This textbook is ideal for graduate students without any particular background in differential equations, but who require an introduction to finite element methods. The author includes a chapter to bridge the gap between mathematics and engineering.
 

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Contents

Chapter I
1
The Maximum Principle
12
A Convergence Theory for Difference Methods
22
Sobolev Spaces
28
Variational Formulation of Elliptic BoundaryValue Problems
34
The Neumann BoundaryValue Problem A Trace Theorem
44
The RitzGalerkin Method and Some Finite Elements
53
Some Standard Finite Elements
60
Chapter IV
177
Gradient Methods
187
Preconditioning
201
Saddle Point Problems
212
Multigrid Methods for Variational Problems
217
Convergence of Multigrid Methods
228
Convergence for Several Levels
239
Nested Iteration
246

Approximation Properties
76
Error Bounds for Elliptic Problems of Second Order
89
Computational Considerations
97
Chapter III
105
Isoparametric Elements
117
Saddle Point Problems
129
Mixed Methods for the Poisson Equation
143
The Stokes Equation
154
A Posteriori Error Estimates
169
Multigrid Analysis via Space Decomposition
252
Nonlinear Problems
263
Chapter VI
269
Hyperelastic Materials
281
Membranes
304
The MindlinReissner Plate
324
References
337
Copyright

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Acta Numerica 1997:
Arieh Iserles
No preview available - 1997
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About the author (2001)

Ruhr-University-Bochum

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